The true answer is somewhere in between. Yes, you get squish, but a radial tire still has the same circumference of rubber around it. This means some of the tread has to slip during the rotation. A bias ply tire can actually stretch and grow with speed.
I saw a video before of a guy who tested that. Same tire, went from 50 down to 10 psi. The radius changed by about 2" on only 30" tire, that's a 13% change in radius, but the measured rotations only changed about 1-2%. Now, this is only one test, but it shows the answer is somewhere in between, it's not a s simple as measuring the circumference, or measuring the radius with weight on the tire.
Since we know the gear ratios are fixed, I just change the tire diameter setting, or the PPM, depending on what the ECU uses, until the speedo is correct. The easiest is to do the ratio of error vs the GPS as
@Blue85 suggested, you can get spot on pretty quick.